Rapid concentration measurement of various metal elements in solutions in a rare earth processing plant or in a nuclear fuel reprocessing plant etc. is an important monitoring technique for efficient processing control. In past years, various assay systems based on gamma absorption, X-ray absorption and X-ray fluorescent densitometry have been developed. However, the rapid on-line measurement of the rare earth concentration in multielement systems has not heretofore been satisfactorily developed. In the late nineteen seventies, research institutes of nuclear engineering in West Germany and Japan, initiated development projects to monitor uranium and plutonium during the processing of nuclear fuel reprocessing plants using K-absorption edge, L-absorption edge and X-ray absorption analysis techniques with success. Shotaro Hayashi et al of Japan in 1985 published a paper on a K-absorption edge analyzer, sometimes called densitometer, including the X-ray generator, a sample solution ell, a Ge detector kept and used at low temperature, a multichannel analyzer and a desk top computer. The X-ray generator was composed of an X-ray controller, a high-voltage power supply and a cooling system. This analyzer or densitomer, however, had the disadvantages of structural complexity, high cost of manufacture, and high expense of operation maintenance, and was hardly applicable to the on-line measurement of individual rare earth components in a multi-system rare-earth mixture--the problem underlying the present invention.